Biomedical subjects

V M Kenkre

Publications and source records attributed to V M Kenkre.

18 recordsLinked to original sources

PubMed2006

Variational formula for the relaxation time in the Boltzmann equation.

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the Boltzmann equation, which allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility for a one-dimensional (1D) tight-binding band indicate that our analysis typically provides a better approximation than the standard RTA.

Journal Article↗

PubMed2005

Patterns and localized structures in population dynamics.

Patterns, fronts, and localized structures of a prototypical model for population dynamics interaction are studied. The physical content of the model is the coexistence of a simple random walk for the motion of the individuals with a nonlinearity in the competitive struggle for resources which simultaneously stresses the Allee effect and interaction at a distance. Mathematically, the model is variational and exhibits coexistence between different stable extended states. Solutions are obtained, the phase diagram is constructed, and the emergence of localized structures is investigated.

Biophysics↗

PubMed2005

Traversal times for random walks on small-world networks.

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate that is different from the rate for steps across small-world connections. When f>>F, the mean time to traverse the network exhibits a transition associated with percolation of the random graph (i.e., small-world) part of the network, and a collapse of the data onto a universal curve. This transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps. We develop a simple self-consistent effective-medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition, as is characteristic of most effective-medium theories.

Journal Article↗

PubMed2005

Theory of home range estimation from displacement measurements of animal populations.

A theory is provided for the estimation of home ranges of animals from displacement measurement procedures. The theoretical tool used is the Fokker-Planck equation, its characteristic quantities being the diffusion constant which describes the motion of the animals, and the attractive potential which addresses their tendency to live in restricted regions, e.g., near their burrows. The measurement technique is shown to correspond to the calculation of a certain kind of mean square displacement of the animals relevant to the specific probing window in space corresponding to the region of observation. The output of the theory is a sigmoid curve of the observable mean square displacement as a function of the ratio of distances characteristic of the home range and the measurement window, along with an explicit prescription to extract the home range from observations. Applications of the theory to rodent movement in Panama and New Mexico are pointed out. An analysis is given of the sensitivity of our theory to the choice of the confining potential via the use of various representative cases. A comparison is provided between home range size inferred from our method and from other procedures employed in the literature. Consequences of home range overlap are also discussed.

Animals↗

PubMed2005

Arbitrary nonlinearities in convective population dynamics with small diffusion.

Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities. The initial-value problem is solved explicitly for some cases, and for others it is shown how to find traveling-wave solutions analytically. The effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity. Using an appropriate small parameter suggested by that analysis, a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion.

Animals↗

PubMed2005

Static pairwise annihilation in complex networks.

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the "hubs" have been annihilated, the network disintegrates and only isolated sites are left.

Journal Article↗

PubMed2005

Diffusion and home range parameters from rodent population measurements in Panama.

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, Zygodontomys brevicauda. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.

Animals↗

PubMed2004

Periodically varying externally imposed environmental effects on population dynamics.

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatiotemporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.

Animals↗

PubMed2004

Multipeaked polarons in soft potentials.

We consider a minimal coupled charge / excitation-lattice model capturing a competition between linear polaronic self-trapping and the self-focusing effects of a soft nonlinear on-site potential. The standard single-humped polaron ceases to exist above a critical value of the coupling strength, closely related to the inflection point in the nonlinear potential. For couplings beyond this critical value, we find that successive multihumped polaronic solutions correspond to the lowest-energy stationary states of the system, which may admit interesting quantum resonance behavior.

Journal Article↗

PubMed2003

Nonlocal interaction effects on pattern formation in population dynamics.

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.

Bacteria↗

PubMed2003

Applicability of the Fisher equation to bacterial population dynamics.

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.

Bacteria↗

PubMed2003

Traveling waves of infection in the hantavirus epidemics.

Traveling waves are analyzed in a model of the hantavirus infection in deer mice. The existence of two kinds of wave phenomena is predicted. An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate. In the other, fronts of susceptible and infected mice travel at the same speed, separated by a constant delay. The dependence of the delay on system parameters is analyzed numerically and through a piecewise linearization.

Animals↗

PubMed2002

Simulations in the mathematical modeling of the spread of the Hantavirus.

The range of validity of a recently proposed deterministic (mean field) model of the spread of the Hantavirus infection is studied with the help of Monte Carlo simulations for the evolution of mice populations. The simulation is found to reproduce earlier results on the average but to display additional behavior stemming from discreteness in mice number and from fluctuations of the finite size system. It is shown that mice diffusion affects those additional features of the simulation in a physically understandable manner, higher diffusion constants leading to greater agreement with the mean field results.

Animals↗

PubMed2002

Spatiotemporal patterns in the Hantavirus infection.

We present a model of the infection of Hantavirus in deer mouse, Peromyscus maniculatus, based on biological observations of the system in the North American Southwest. The results of the analysis shed light on relevant observations of the biological system, such as the sporadical disappearance of the infection, and the existence of foci or "refugia" that perform as reservoirs of the virus when environmental conditions are less than optimal.

Animals↗

PubMed2001

Effects of transport memory and nonlinear damping in a generalized Fisher's equation.

Memory effects in transport require, for their incorporation into reaction-diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects, and traveling wave solutions of the equation are found. Comparison is made with alternative generalization procedures.

Journal Article↗

PubMed2001

Nature of charge carriers in disordered molecular solids: are polarons compatible with observations?

Polaronic theories for charge transport in disordered organic solids, particularly molecularly doped polymers, have been plagued by issues of internal consistency related to the magnitude of physical parameters. We present a natural resolution of the problem by showing that, in the presence of correlated disorder, polaronic carriers with binding energies Delta approximately 50-500 meV and transfer integrals J approximately 1-20 meV are completely consistent with the magnitudes of field and temperature dependent mobilities observed.

Journal Article↗

PubMed1999

Nature of transitions in augmented discrete nonlinear Schrödinger equations.

We investigate the nature of the transitions between free and self-trapping states occurring in systems described by augmented forms of the discrete nonlinear Schrödinger equation. These arise from an interaction between a moving quasiparticle (such as an electron or an exciton) and lattice vibrations, when the effects of nonlinearities in interaction potential and restoring force are included. We derive analytic conditions for the stability of the free state and the crossover between first- and second-order transitions. We demonstrate our results for different types of nonlinearities in the interaction potential and restoring force. We find that, depending on the type of nonlinearity, it is possible to have both first- and second-order transitions. We discuss possible hysteresis effects.

Journal Article↗

PubMed1992

Theoretical framework for the interpretation of STM images of adsorbates.

A theoretical formalism for the interpretation of STM images of adsorbates is developed by approaching the calculation of the observed current as a transport problem in quantum statistical mechanics. The STM configuration is treated as a system of three groups of states--the substrate, the adsorbate and the tip--in contact with a thermal reservoir, with which it exchanges energy. A new definition of current is introduced, and shown to be related to that given in the traditional transfer Hamiltonian approach. The transport instrument used for the description is the stochastic Liouville equation, known to have the advantage of allowing the incorporation of thermal effects as well as arbitrary degree of coherence in the quantum transport. Some preliminary calculations of STM images of simple adsorbate models are presented.

Computer Simulation↗